Roberto Mancini held his first meeting with new Director of Football Txiki Begiristain earlier this week and the pair have put the Italian international at the top of their list of targets.
The 29-year-old is believed to be unsettled in Rome following the arrival of new coach Zdenek Zemen.
Under the Czech manager De Rossi has been played out of position on the right hand side of a 4-3-3 formation, which has left the local hero disillusioned and frustrated.
City failed with an approach to sign the holding midfielder over the summer, as he pledged his commitment to the club.
However, Mancini believes he may now be able to entice his target to the Etihad Stadium by taking advantage of his unrest.
Paris Saint-Germain are also said to be monitoring the situation and could rival any approach from the Citizens.
De Rossi was a key member of the Italian squad during EURO 2012. His displays in the centre of the park aided the team on their journey to the final, which they eventually lost to Spain.
Although he is a central midfielder by trade, the Roma vice-captain has been known to play as part of a three-man defence, which may appeal to the Premier League champions who have adopted the same system on multiple occasions this season.